I can’t figure out why it won’t let me move things from my main folder to any subfolders.

FTP is really nothing more than the ability to upload or download files. Moving files is another matter entirely. You can drag stuff from your local drive to the server, but not (normally) from one place on the server to another.

So to move a file from one place on the server to another, drag it to a local folder and then drag it back to the new location. You will then have to delete the file from the original location.

I usually create a directory structure on my local drive that matches the one that will exist on the server.